At the end of install select the "Advanced" button (probably the same place you selected to not install Grub) and this should give choice of installing grub on the USB key by choosing the correct device.

You could try Super Grub rather than reinstalling, as it can apparently boot a kernel directly, then fix Grub from there.

Also some USB flash drives are notorious for having problems with corrupted master boot records, one I definitely know of is the Kingston Data Traveler. To fix can use apt package called mbr. fdisk -l (to locate drive) then install-mbr /dev/sdx (with sdx being flash device)